Abstract

We demonstrated the Talbot effect using a broadband hard x-ray beam (Δλ/λ ~1). The exit wave-field of the x-ray beam passing through a grating with a sub micro-meter scale period was successfully replicated and recorded at effective Talbot distance, ZT. The period was reduced to half at ZT/4 and 3/4ZT, and the phase reversal was observed at ZT/2. The propagating wave-field recorded on photoresists was consistent with a simulated result.

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  1. H. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).
  2. L. Rayleigh, “On Copying Diffraction-Gratings, and some Phenomena Connected Therewith,” Philos. Mag. 11, 196 (1881).
  3. M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
    [CrossRef] [PubMed]
  4. L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
    [CrossRef]
  5. B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
    [CrossRef] [PubMed]
  6. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).
  7. W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
    [CrossRef] [PubMed]
  8. W. B. Case, M. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot-Lau configurations,” Opt. Express 17(23), 20966–20974 (2009).
    [CrossRef] [PubMed]
  9. N. Guérineau, E. Di Mambro, J. Primot, and F. Alves, “Talbot experiment re-examined: study of the chromatic regime and application to spectrometry,” Opt. Express 11(24), 3310–3319 (2003).
    [CrossRef] [PubMed]
  10. P. Cloetens, J. P. Guigay, C. De Martino, J. Baruchel, and M. Schlenker, “Fractional Talbot imaging of phase gratings with hard x rays,” Opt. Lett. 22(14), 1059–1061 (1997).
    [CrossRef] [PubMed]
  11. C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
    [CrossRef]
  12. H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
    [CrossRef] [PubMed]
  13. Filter Transmission, http://henke.lbl.gov/optical_constants/filter2.html
  14. K. Lee and S. S. Lee, “Deep X-ray mask with integrated actuator for 3D microfabrication,” Sens. Actuators A Phys. 108(1-3), 121–127 (2003).
    [CrossRef]
  15. J. W. Goodman, Introduction to Fourier optics (Roberts & Company, 2005).
  16. K. Suzuki, and B. W. Smith, Microlithography: Science and Technology (CRC Press, 2007).
  17. X-ray Form Factor, Attenuation, and Scattering Tables, http://physics.nist.gov/cgi-bin/ffast/ffast.pl?Z=14&Formula=&gtype=5&range=S&lower=2.4848&upper=24.848&density=2.33

2009

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

W. B. Case, M. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot-Lau configurations,” Opt. Express 17(23), 20966–20974 (2009).
[CrossRef] [PubMed]

2007

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

2006

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

2005

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

2003

2002

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

1999

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

1997

1995

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

1881

L. Rayleigh, “On Copying Diffraction-Gratings, and some Phenomena Connected Therewith,” Philos. Mag. 11, 196 (1881).

1836

H. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).

Alves, F.

Arndt, M.

W. B. Case, M. Tomandl, S. Deachapunya, and M. Arndt, “Realization of optical carpets in the Talbot and Talbot-Lau configurations,” Opt. Express 17(23), 20966–20974 (2009).
[CrossRef] [PubMed]

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Baruchel, J.

Brezger, B.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Bunk, O.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Case, W. B.

Chapman, M. S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Clark, C. W.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Cloetens, P.

Conley, R.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

David, C.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

De Martino, C.

Deachapunya, S.

Deng, L.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Denschlag, J.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Di Mambro, E.

Edwards, M.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Ekstrom, C. R.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Guérineau, N.

Guigay, J. P.

Hackermüller, L.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Hagley, E. W.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Hammond, T. D.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Helmerson, K.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Hiller, J.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Kang, H. C.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Khachatryan, R.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Koritala, R.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Lee, K.

K. Lee and S. S. Lee, “Deep X-ray mask with integrated actuator for 3D microfabrication,” Sens. Actuators A Phys. 108(1-3), 121–127 (2003).
[CrossRef]

Lee, S. S.

K. Lee and S. S. Lee, “Deep X-ray mask with integrated actuator for 3D microfabrication,” Sens. Actuators A Phys. 108(1-3), 121–127 (2003).
[CrossRef]

Liu, C.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Macrander, A. T.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Maser, J.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Momose, A.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Petschinka, J.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Pfeiffer, F.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Phillips, W. D.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Primot, J.

Pritchard, D. E.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Rayleigh, L.

L. Rayleigh, “On Copying Diffraction-Gratings, and some Phenomena Connected Therewith,” Philos. Mag. 11, 196 (1881).

Rolston, S. L.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Schlenker, M.

Schmiedmayer, J.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Simsarian, J. E.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

Stephenson, G. B.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Suzuki, Y.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Takeda, Y.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Takeuchi, A.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Talbot, H. F.

H. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).

Tannian, B. E.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Tomandl, M.

Uttenthaler, S.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Wehinger, S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Weitkamp, T.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Wieczorek, M.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Yan, H.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Yashiro, W.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Zeilinger, A.

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

Zurbuchen, M. A.

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

J. Appl. Phys.

C. Liu, R. Conley, A. T. Macrander, J. Maser, H. C. Kang, M. A. Zurbuchen, and G. B. Stephenson, “Depth-graded multilayers for application in transmission geometry as linear zone plates,” J. Appl. Phys. 98(11), 113519 (2005).
[CrossRef]

Nature

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).

Opt. Express

Opt. Lett.

Philos. Mag.

H. F. Talbot, “Facts Relating to Optical Science,” Philos. Mag. 9, 401–407 (1836).

L. Rayleigh, “On Copying Diffraction-Gratings, and some Phenomena Connected Therewith,” Philos. Mag. 11, 196 (1881).

Phys. Rev. A

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A 51(1), R14–R17 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett.

L. Deng, E. W. Hagley, J. Denschlag, J. E. Simsarian, M. Edwards, C. W. Clark, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Temporal, Matter-Wave-Dispersion Talbot Effect,” Phys. Rev. Lett. 83(26), 5407–5411 (1999).
[CrossRef]

B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, “Matter-wave interferometer for large molecules,” Phys. Rev. Lett. 88(10), 100404 (2002).
[CrossRef] [PubMed]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating,” Phys. Rev. Lett. 103(18), 180801 (2009).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

H. C. Kang, G. B. Stephenson, C. Liu, R. Conley, R. Khachatryan, M. Wieczorek, A. T. Macrander, H. Yan, J. Maser, J. Hiller, and R. Koritala, “Sectioning of multilayers to make a multilayer Laue lens,” Rev. Sci. Instrum. 78(4), 046103 (2007).
[CrossRef] [PubMed]

Sens. Actuators A Phys.

K. Lee and S. S. Lee, “Deep X-ray mask with integrated actuator for 3D microfabrication,” Sens. Actuators A Phys. 108(1-3), 121–127 (2003).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier optics (Roberts & Company, 2005).

K. Suzuki, and B. W. Smith, Microlithography: Science and Technology (CRC Press, 2007).

X-ray Form Factor, Attenuation, and Scattering Tables, http://physics.nist.gov/cgi-bin/ffast/ffast.pl?Z=14&Formula=&gtype=5&range=S&lower=2.4848&upper=24.848&density=2.33

Filter Transmission, http://henke.lbl.gov/optical_constants/filter2.html

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Figures (5)

Fig. 1
Fig. 1

Schematic view of the Talbot effect. The grating image is replicated at the Talbot distance, ZT while its phase is reversed at ZT/2. The period of the wave-field intensity reduces to half the grating period at ZT/4 and 3ZT/4.

Fig. 2
Fig. 2

(a) Schematic illustration of the experimental configuration. (b) SEM image of the sectioned Si/WSi2 multilayer grating. The bright and dark regions represent WSi2 and Si respectively. (c) Transmittance through the transparent Si and the opaque WSi2 regions. (d) Broken red line represents the spectral density of the bending magnet and the solid line represents the spectral density of the polychromatic beam incident on the multilayer mask.

Fig. 3
Fig. 3

Simulated wave-field intensity downstream of a periodic grating under broadband illumination (a) and monochromatic illumination (b). We used the grating structure and the spectral density used in this experiment. For the monochromatic case, the averaged wavelength obtained from the spectral density was used.

Fig. 4
Fig. 4

Wave-field intensity recorded on PR at 0.2 mm(a), 1.4 mm(b), 2.8 mm(c), 4.2 mm (d), 5.6 mm (e) downstream of the grating. On the right is the simulated result for comparison.

Fig. 5
Fig. 5

Recorded wavefield intensity in the near field region (a) and at half the Talbot distance (b). The number of line patterns is reduced by one in (b) due to phase shift of electric field. The observed phase shift is consistent with the line profile of the simulated intensity profile in the near field (c) and at half the Talbot distance (d). Dashed line indicates the relative phase shift between the two regions.

Equations (5)

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h ( X , Y ;     λ ) = e i k z i λ z e i k 2 z ( X 2 + Y 2 ) ,
g ( X , Y ;     λ ) = e i k z i λ z f ( x , y ; λ ) e i k 2 z [ ( X x ) 2 + ( Y y ) 2 ] d x d y .
E t o t a l ( X , Y ) = B ( λ ) g ( X , Y ;     λ ) d λ ,
I ( X , Y ) = | B ( λ ) | 2 | g ( X , Y ;     λ ) | 2 S ( λ ) d λ .
λ a v = ( λ | B ( λ ) | 2 T ( λ ) S ( λ ) λ 2 d λ ) / ( | B ( λ ) | 2 T ( λ ) S ( λ ) λ 2 d λ ) ,

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